Cohomology of group number 866 of order 128

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

General information on the group

  • The group has 3 minimal generators and exponent 8.
  • It is non-abelian.
  • It has p-Rank 4.
  • Its center has rank 1.
  • It has 3 conjugacy classes of maximal elementary abelian subgroups, which are of rank 3, 3 and 4, respectively.

Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 4 and depth 2.
  • The depth exceeds the Duflot bound, which is 1.
  • The Poincaré series is
    t5  −  t4  +  t2  −  t  +  1
    (t  −  1)4 · (t2  +  1) · (t4  +  1)
  • The a-invariants are -∞,-∞,-5,-4,-4. They were obtained using the filter regular HSOP of the Benson test.

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Ring generators

The cohomology ring has 14 minimal generators of maximal degree 8:

  1. a_1_0, a nilpotent element of degree 1
  2. b_1_1, an element of degree 1
  3. b_1_2, an element of degree 1
  4. b_2_4, an element of degree 2
  5. b_2_5, an element of degree 2
  6. b_3_8, an element of degree 3
  7. b_3_9, an element of degree 3
  8. b_3_10, an element of degree 3
  9. b_4_16, an element of degree 4
  10. b_5_22, an element of degree 5
  11. b_5_23, an element of degree 5
  12. b_6_32, an element of degree 6
  13. b_7_43, an element of degree 7
  14. c_8_57, a Duflot regular element of degree 8

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Ring relations

There are 51 minimal relations of maximal degree 14:

  1. a_1_02
  2. a_1_0·b_1_1
  3. a_1_0·b_1_22 + b_2_4·a_1_0
  4. b_2_4·b_1_1 + b_2_5·a_1_0
  5. b_2_5·b_1_1 + b_2_4·b_1_1
  6. b_2_52 + b_2_4·b_1_22 + b_2_4·b_2_5 + b_2_42 + b_2_5·a_1_0·b_1_2
  7. a_1_0·b_3_8
  8. b_2_4·b_1_22 + b_2_42 + a_1_0·b_3_9 + b_2_5·a_1_0·b_1_2
  9. b_1_1·b_3_9 + b_1_1·b_3_8 + b_2_5·b_1_22 + b_2_52 + b_2_4·b_1_22 + b_2_42
  10. b_2_5·b_1_22 + b_2_52 + b_2_4·b_1_22 + b_2_42 + a_1_0·b_3_10
  11. b_2_5·b_3_8 + b_2_4·b_2_5·a_1_0
  12. b_2_4·b_3_8 + b_2_4·b_2_5·a_1_0
  13. b_2_5·b_3_10 + b_2_5·b_3_9
  14. b_1_22·b_3_9 + b_1_22·b_3_8 + b_2_4·b_3_9 + a_1_0·b_1_2·b_3_10
  15. b_2_5·b_3_9 + b_2_4·b_3_10 + b_2_4·b_2_5·a_1_0
  16. b_1_22·b_3_9 + b_1_22·b_3_8 + b_2_4·b_3_9 + a_1_0·b_1_2·b_3_9 + b_4_16·a_1_0
       + b_2_4·b_2_5·a_1_0
  17. b_3_8·b_3_9 + b_3_82 + b_2_4·a_1_0·b_3_10
  18. b_3_9·b_3_10 + b_3_8·b_3_10 + b_2_5·b_4_16
  19. b_3_92 + b_3_82 + b_2_4·b_1_2·b_3_10 + b_2_4·b_1_2·b_3_9 + b_2_4·b_4_16
  20. b_3_82 + b_1_26 + b_1_1·b_1_22·b_3_8 + b_1_1·b_1_25 + b_1_12·b_1_2·b_3_10
       + b_1_12·b_1_2·b_3_8 + b_1_13·b_3_10 + b_1_13·b_3_8 + b_4_16·b_1_12 + b_2_43
       + b_2_4·a_1_0·b_3_9
  21. b_3_8·b_3_9 + b_3_82 + a_1_0·b_5_22
  22. b_3_102 + b_3_9·b_3_10 + b_3_92 + b_3_8·b_3_10 + b_1_23·b_3_10 + b_1_1·b_5_22
       + b_1_1·b_1_22·b_3_8 + b_1_1·b_1_25 + b_1_12·b_1_2·b_3_10 + b_1_12·b_1_2·b_3_8
       + b_1_13·b_3_10 + b_1_13·b_3_8 + b_1_13·b_1_23 + b_4_16·b_1_22
       + b_4_16·b_1_1·b_1_2 + b_2_4·b_1_2·b_3_9
  23. b_3_8·b_3_9 + b_3_82 + a_1_0·b_5_23 + b_2_4·b_2_5·a_1_0·b_1_2
  24. b_3_102 + b_3_9·b_3_10 + b_3_92 + b_3_8·b_3_10 + b_3_8·b_3_9 + b_3_82 + b_1_23·b_3_10
       + b_1_1·b_5_23 + b_1_1·b_1_22·b_3_10 + b_1_12·b_1_2·b_3_8 + b_1_12·b_1_24
       + b_1_13·b_1_23 + b_4_16·b_1_22 + b_4_16·b_1_1·b_1_2 + b_2_4·b_1_2·b_3_9
  25. b_2_5·b_5_22 + b_2_42·b_3_10 + b_2_4·a_1_0·b_1_2·b_3_9 + b_2_4·b_4_16·a_1_0
       + b_2_42·b_2_5·a_1_0
  26. b_1_22·b_5_23 + b_1_22·b_5_22 + b_1_24·b_3_10 + b_1_24·b_3_8 + b_1_27
       + b_1_1·b_1_23·b_3_10 + b_1_1·b_1_26 + b_1_12·b_1_22·b_3_10
       + b_1_12·b_1_22·b_3_8 + b_2_5·b_5_23 + b_2_4·b_5_22 + b_2_42·b_3_10 + b_2_43·b_1_2
       + b_2_4·b_4_16·a_1_0
  27. b_2_5·b_5_23 + b_2_4·b_5_23 + b_2_4·a_1_0·b_1_2·b_3_9 + b_2_4·b_4_16·a_1_0
  28. b_6_32·a_1_0 + b_2_4·b_4_16·a_1_0
  29. b_1_2·b_3_8·b_3_10 + b_1_22·b_5_22 + b_1_24·b_3_10 + b_1_1·b_3_8·b_3_10
       + b_1_1·b_1_23·b_3_10 + b_1_12·b_5_22 + b_1_12·b_1_22·b_3_10 + b_1_13·b_1_2·b_3_10
       + b_1_13·b_1_24 + b_1_14·b_3_8 + b_1_14·b_1_23 + b_1_15·b_1_22 + b_6_32·b_1_1
       + b_4_16·b_3_8 + b_4_16·b_1_1·b_1_22 + b_2_4·b_5_22 + b_2_42·b_3_10
       + b_2_4·a_1_0·b_1_2·b_3_9 + b_2_4·b_4_16·a_1_0 + b_2_42·b_2_5·a_1_0
  30. b_3_9·b_5_23 + b_3_8·b_5_23 + b_2_5·b_6_32 + b_2_4·b_1_2·b_5_23 + b_2_43·b_2_5
       + b_2_42·a_1_0·b_3_10 + b_2_42·a_1_0·b_3_9
  31. b_3_8·b_5_23 + b_3_8·b_5_22 + b_1_23·b_5_22 + b_1_25·b_3_10 + b_1_25·b_3_8 + b_1_28
       + b_1_1·b_1_24·b_3_10 + b_1_1·b_1_27 + b_1_12·b_3_8·b_3_10 + b_1_12·b_1_2·b_5_22
       + b_1_12·b_1_23·b_3_8 + b_1_12·b_1_26 + b_1_14·b_1_2·b_3_10 + b_1_14·b_1_24
       + b_1_15·b_3_10 + b_1_15·b_3_8 + b_1_15·b_1_23 + b_6_32·b_1_1·b_1_2
       + b_4_16·b_1_2·b_3_8 + b_4_16·b_1_1·b_1_23 + b_4_16·b_1_12·b_1_22
       + b_4_16·b_1_14 + b_2_4·b_1_2·b_5_22 + b_2_42·b_1_2·b_3_10 + b_2_44
       + b_2_42·b_2_5·a_1_0·b_1_2
  32. b_3_9·b_5_23 + b_3_9·b_5_22 + b_3_8·b_5_23 + b_3_8·b_5_22 + b_2_4·b_1_2·b_5_23
       + b_2_4·b_6_32 + b_2_42·b_4_16 + b_2_43·b_2_5 + b_2_42·a_1_0·b_3_9
       + b_2_42·b_2_5·a_1_0·b_1_2
  33. b_3_10·b_5_23 + b_3_10·b_5_22 + b_3_9·b_5_23 + b_3_8·b_5_22 + b_1_25·b_3_8
       + b_1_1·b_1_24·b_3_10 + b_1_12·b_3_8·b_3_10 + b_1_12·b_1_2·b_5_22
       + b_1_12·b_1_23·b_3_10 + b_1_12·b_1_23·b_3_8 + b_1_14·b_1_2·b_3_8 + b_1_15·b_3_10
       + b_1_16·b_1_22 + b_6_32·b_1_12 + b_4_16·b_1_24 + b_4_16·b_1_1·b_3_8
       + b_4_16·b_1_12·b_1_22 + b_2_4·b_2_5·b_4_16 + b_2_42·b_4_16
  34. a_1_0·b_7_43 + b_2_42·a_1_0·b_3_10 + b_2_42·b_2_5·a_1_0·b_1_2
  35. b_3_10·b_5_23 + b_3_10·b_5_22 + b_3_9·b_5_23 + b_1_23·b_5_22 + b_1_25·b_3_8
       + b_1_1·b_7_43 + b_1_1·b_1_24·b_3_8 + b_1_12·b_3_8·b_3_10 + b_1_12·b_1_23·b_3_10
       + b_1_12·b_1_23·b_3_8 + b_1_13·b_1_22·b_3_10 + b_1_13·b_1_22·b_3_8
       + b_1_13·b_1_25 + b_1_14·b_1_2·b_3_10 + b_1_14·b_1_2·b_3_8 + b_1_14·b_1_24
       + b_1_15·b_3_10 + b_4_16·b_1_2·b_3_8 + b_4_16·b_1_1·b_3_10 + b_4_16·b_1_12·b_1_22
       + b_4_16·b_1_14 + b_2_4·b_1_2·b_5_22 + b_2_4·b_2_5·b_4_16 + b_2_42·a_1_0·b_3_10
       + b_2_42·b_2_5·a_1_0·b_1_2
  36. b_6_32·b_3_9 + b_6_32·b_3_8 + b_4_16·b_5_23 + b_4_16·b_5_22 + b_4_16·b_1_22·b_3_10
       + b_4_16·b_1_22·b_3_8 + b_4_16·b_1_25 + b_4_16·b_1_1·b_1_2·b_3_10
       + b_4_16·b_1_1·b_1_24 + b_4_16·b_1_12·b_3_10 + b_4_16·b_1_12·b_3_8
       + b_2_4·b_6_32·b_1_2 + b_2_4·b_4_16·b_3_10 + b_2_4·b_4_16·b_3_9
       + b_2_4·b_2_5·b_4_16·b_1_2 + b_2_42·b_5_23 + b_2_43·b_3_10 + b_2_43·b_2_5·b_1_2
       + b_2_42·a_1_0·b_1_2·b_3_9 + b_2_43·b_2_5·a_1_0
  37. b_2_5·b_7_43 + b_2_5·b_6_32·b_1_2 + b_2_4·b_2_5·b_4_16·b_1_2 + b_2_43·b_3_10
       + b_2_43·b_2_5·b_1_2 + b_2_42·b_4_16·a_1_0 + b_2_43·b_2_5·a_1_0
  38. b_2_4·b_7_43 + b_2_4·b_6_32·b_1_2 + b_2_4·b_2_5·b_4_16·b_1_2 + b_2_43·b_3_9
       + b_2_43·b_2_5·b_1_2 + b_2_42·b_4_16·a_1_0
  39. b_1_22·b_7_43 + b_1_24·b_5_22 + b_1_26·b_3_10 + b_1_26·b_3_8 + b_1_1·b_1_23·b_5_22
       + b_1_1·b_1_28 + b_1_12·b_7_43 + b_1_12·b_1_22·b_5_22 + b_1_12·b_1_24·b_3_10
       + b_1_12·b_1_24·b_3_8 + b_1_13·b_1_2·b_5_22 + b_1_13·b_1_26 + b_1_14·b_1_25
       + b_1_15·b_1_2·b_3_10 + b_1_15·b_1_2·b_3_8 + b_1_16·b_3_10 + b_6_32·b_3_8
       + b_6_32·b_1_23 + b_4_16·b_1_22·b_3_10 + b_4_16·b_1_1·b_1_24
       + b_4_16·b_1_12·b_3_10 + b_4_16·b_1_12·b_3_8 + b_4_16·b_1_12·b_1_23
       + b_4_16·b_1_14·b_1_2 + b_4_16·b_1_15 + b_4_162·b_1_1 + b_2_4·b_4_16·b_3_10
       + b_2_4·b_2_5·b_4_16·b_1_2 + b_2_42·b_5_22 + b_2_43·b_3_10 + b_2_43·b_3_9
       + b_2_43·b_2_5·b_1_2 + b_2_42·b_4_16·a_1_0
  40. b_5_232 + b_5_222 + b_1_27·b_3_10 + b_1_210 + b_1_1·b_1_24·b_5_22
       + b_1_1·b_1_26·b_3_8 + b_1_1·b_1_29 + b_1_12·b_1_25·b_3_8 + b_1_13·b_1_22·b_5_22
       + b_1_13·b_1_24·b_3_10 + b_1_13·b_1_24·b_3_8 + b_1_13·b_1_27
       + b_1_14·b_1_23·b_3_10 + b_1_15·b_5_22 + b_1_15·b_1_22·b_3_8
       + b_1_16·b_1_2·b_3_10 + b_1_16·b_1_2·b_3_8 + b_1_17·b_3_10 + b_1_17·b_3_8
       + b_1_17·b_1_23 + b_4_16·b_1_26 + b_4_16·b_1_1·b_1_25 + b_4_16·b_1_12·b_1_24
       + b_4_16·b_1_13·b_1_23 + b_4_16·b_1_15·b_1_2 + b_2_4·b_4_162
       + b_2_42·b_2_5·b_4_16 + b_2_43·b_1_2·b_3_9 + b_2_45 + b_2_43·a_1_0·b_3_10
       + b_2_43·a_1_0·b_3_9
  41. b_5_22·b_5_23 + b_5_222 + b_1_25·b_5_22 + b_1_27·b_3_8 + b_1_210
       + b_1_1·b_1_2·b_3_10·b_5_22 + b_1_1·b_1_26·b_3_8 + b_1_1·b_1_29
       + b_1_12·b_1_2·b_7_43 + b_1_12·b_1_25·b_3_10 + b_1_12·b_1_25·b_3_8
       + b_1_13·b_7_43 + b_1_13·b_1_22·b_5_22 + b_1_13·b_1_24·b_3_10
       + b_1_13·b_1_24·b_3_8 + b_1_14·b_3_8·b_3_10 + b_1_14·b_1_23·b_3_10
       + b_1_14·b_1_23·b_3_8 + b_1_14·b_1_26 + b_1_16·b_1_2·b_3_10 + b_1_16·b_1_2·b_3_8
       + b_1_17·b_3_10 + b_1_17·b_1_23 + b_6_32·b_1_1·b_3_10 + b_6_32·b_1_1·b_3_8
       + b_6_32·b_1_12·b_1_22 + b_6_32·b_1_13·b_1_2 + b_4_16·b_3_8·b_3_10
       + b_4_16·b_1_23·b_3_8 + b_4_16·b_1_1·b_1_22·b_3_10 + b_4_16·b_1_12·b_1_2·b_3_10
       + b_4_16·b_1_12·b_1_2·b_3_8 + b_4_16·b_1_13·b_3_10 + b_4_16·b_1_14·b_1_22
       + b_4_16·b_1_15·b_1_2 + b_4_16·b_1_16 + b_4_162·b_1_12 + b_2_5·b_4_162
       + b_2_4·b_4_162 + b_2_4·b_2_5·b_6_32 + b_2_42·b_1_2·b_5_23 + b_2_42·b_1_2·b_5_22
       + b_2_43·b_1_2·b_3_10 + b_2_43·b_1_2·b_3_9 + b_2_43·b_4_16 + b_2_44·b_2_5 + b_2_45
  42. b_3_8·b_7_43 + b_1_27·b_3_10 + b_1_210 + b_1_1·b_1_2·b_3_10·b_5_22
       + b_1_1·b_1_26·b_3_8 + b_1_12·b_3_10·b_5_22 + b_1_12·b_1_2·b_7_43
       + b_1_12·b_1_23·b_5_22 + b_1_12·b_1_25·b_3_10 + b_1_12·b_1_28 + b_1_13·b_1_27
       + b_1_14·b_3_8·b_3_10 + b_1_14·b_1_26 + b_1_15·b_5_22 + b_1_15·b_1_22·b_3_8
       + b_1_15·b_1_25 + b_1_16·b_1_2·b_3_8 + b_1_17·b_3_10 + b_1_17·b_3_8
       + b_1_17·b_1_23 + b_6_32·b_1_2·b_3_8 + b_6_32·b_1_24 + b_6_32·b_1_1·b_1_23
       + b_4_16·b_3_8·b_3_10 + b_4_16·b_1_26 + b_4_16·b_1_1·b_5_22
       + b_4_16·b_1_1·b_1_22·b_3_10 + b_4_16·b_1_1·b_1_25 + b_4_16·b_1_12·b_1_2·b_3_10
       + b_4_16·b_1_12·b_1_24 + b_4_16·b_1_13·b_3_10 + b_4_16·b_1_13·b_3_8
       + b_2_42·b_6_32 + b_2_43·b_1_2·b_3_10 + b_2_43·b_4_16 + b_2_45 + b_2_43·a_1_0·b_3_9
  43. b_3_9·b_7_43 + b_1_27·b_3_10 + b_1_210 + b_1_1·b_1_2·b_3_10·b_5_22
       + b_1_1·b_1_26·b_3_8 + b_1_12·b_3_10·b_5_22 + b_1_12·b_1_2·b_7_43
       + b_1_12·b_1_23·b_5_22 + b_1_12·b_1_25·b_3_10 + b_1_12·b_1_28 + b_1_13·b_1_27
       + b_1_14·b_3_8·b_3_10 + b_1_14·b_1_26 + b_1_15·b_5_22 + b_1_15·b_1_22·b_3_8
       + b_1_15·b_1_25 + b_1_16·b_1_2·b_3_8 + b_1_17·b_3_10 + b_1_17·b_3_8
       + b_1_17·b_1_23 + b_6_32·b_1_2·b_3_8 + b_6_32·b_1_24 + b_6_32·b_1_1·b_1_23
       + b_4_16·b_3_8·b_3_10 + b_4_16·b_1_2·b_5_23 + b_4_16·b_1_2·b_5_22
       + b_4_16·b_1_23·b_3_10 + b_4_16·b_1_23·b_3_8 + b_4_16·b_1_1·b_5_22
       + b_4_16·b_1_12·b_1_2·b_3_8 + b_4_16·b_1_12·b_1_24 + b_4_16·b_1_13·b_3_10
       + b_4_16·b_1_13·b_3_8 + b_2_4·b_4_16·b_1_2·b_3_9 + b_2_42·b_1_2·b_5_23
       + b_2_42·b_2_5·b_4_16 + b_2_43·b_1_2·b_3_9 + b_2_44·b_2_5 + b_2_45
       + b_2_43·a_1_0·b_3_10
  44. b_5_222 + b_1_1·b_1_2·b_3_10·b_5_22 + b_1_12·b_1_23·b_5_22
       + b_1_13·b_1_24·b_3_10 + b_1_13·b_1_27 + b_1_14·b_1_23·b_3_8
       + b_1_15·b_1_22·b_3_10 + b_1_15·b_1_22·b_3_8 + b_1_16·b_1_2·b_3_10
       + b_1_16·b_1_2·b_3_8 + b_1_16·b_1_24 + b_1_17·b_1_23 + b_1_18·b_1_22
       + b_6_32·b_1_12·b_1_22 + b_6_32·b_1_13·b_1_2 + b_6_32·b_1_14
       + b_4_16·b_1_1·b_5_22 + b_4_16·b_1_1·b_1_22·b_3_10 + b_4_16·b_1_12·b_1_2·b_3_10
       + b_4_16·b_1_12·b_1_2·b_3_8 + b_4_16·b_1_13·b_3_10 + b_4_16·b_1_13·b_3_8
       + b_4_16·b_1_16 + b_4_162·b_1_22 + b_4_162·b_1_1·b_1_2 + b_4_162·b_1_12
       + b_2_5·b_4_162 + b_2_43·b_1_2·b_3_10 + b_2_43·b_1_2·b_3_9 + b_2_43·b_4_16
       + b_2_43·b_2_5·a_1_0·b_1_2 + c_8_57·b_1_12
  45. b_6_32·b_5_23 + b_6_32·b_5_22 + b_6_32·b_1_22·b_3_10 + b_6_32·b_1_22·b_3_8
       + b_6_32·b_1_25 + b_6_32·b_1_1·b_1_2·b_3_10 + b_6_32·b_1_1·b_1_24
       + b_6_32·b_1_12·b_3_10 + b_6_32·b_1_12·b_3_8 + b_4_162·b_3_9 + b_4_162·b_3_8
       + b_2_5·b_4_162·b_1_2 + b_2_4·b_4_16·b_5_22 + b_2_42·b_6_32·b_1_2
       + b_2_42·b_4_16·b_3_10 + b_2_42·b_4_16·b_3_9 + b_2_43·b_5_23 + b_2_43·b_4_16·b_1_2
       + b_2_44·b_3_10 + b_2_44·b_3_9 + b_2_43·a_1_0·b_1_2·b_3_9 + b_2_43·b_4_16·a_1_0
       + b_2_44·b_2_5·a_1_0
  46. b_1_2·b_3_10·b_7_43 + b_1_28·b_3_8 + b_1_1·b_3_10·b_7_43 + b_1_1·b_1_27·b_3_8
       + b_1_12·b_1_26·b_3_10 + b_1_12·b_1_29 + b_1_13·b_1_2·b_7_43
       + b_1_13·b_1_23·b_5_22 + b_1_13·b_1_25·b_3_8 + b_1_14·b_1_24·b_3_8
       + b_1_14·b_1_27 + b_1_15·b_3_8·b_3_10 + b_1_15·b_1_2·b_5_22
       + b_1_15·b_1_23·b_3_10 + b_1_15·b_1_23·b_3_8 + b_1_15·b_1_26 + b_1_16·b_5_22
       + b_1_16·b_1_22·b_3_10 + b_1_16·b_1_22·b_3_8 + b_1_17·b_1_24 + b_1_18·b_3_10
       + b_1_18·b_3_8 + b_1_18·b_1_23 + b_1_19·b_1_22 + b_6_32·b_5_23
       + b_6_32·b_1_22·b_3_10 + b_6_32·b_1_22·b_3_8 + b_6_32·b_1_25
       + b_6_32·b_1_1·b_1_2·b_3_10 + b_6_32·b_1_15 + b_4_16·b_7_43 + b_4_16·b_1_24·b_3_10
       + b_4_16·b_1_27 + b_4_16·b_1_1·b_3_8·b_3_10 + b_4_16·b_1_1·b_1_2·b_5_22
       + b_4_16·b_1_12·b_1_22·b_3_8 + b_4_16·b_1_12·b_1_25 + b_4_16·b_1_13·b_1_2·b_3_8
       + b_4_16·b_1_13·b_1_24 + b_4_16·b_1_14·b_1_23 + b_4_16·b_1_16·b_1_2
       + b_4_16·b_1_17 + b_4_16·b_6_32·b_1_2 + b_4_16·b_6_32·b_1_1 + b_4_162·b_3_10
       + b_4_162·b_3_8 + b_4_162·b_1_23 + b_4_162·b_1_12·b_1_2 + b_2_4·b_4_162·b_1_2
       + b_2_42·b_6_32·b_1_2 + b_2_42·b_4_16·b_3_10 + b_2_42·b_4_16·b_3_9
       + b_2_42·b_2_5·b_4_16·b_1_2 + b_2_43·b_5_23 + b_2_43·b_4_16·b_1_2 + b_2_44·b_3_10
       + b_2_43·a_1_0·b_1_2·b_3_9 + b_2_43·b_4_16·a_1_0 + b_2_44·b_2_5·a_1_0
       + c_8_57·b_1_1·b_1_22 + c_8_57·b_1_13 + b_2_5·c_8_57·a_1_0
  47. b_5_23·b_7_43 + b_5_22·b_7_43 + b_1_27·b_5_22 + b_1_212 + b_1_12·b_3_10·b_7_43
       + b_1_12·b_1_25·b_5_22 + b_1_12·b_1_27·b_3_8 + b_1_13·b_1_24·b_5_22
       + b_1_13·b_1_26·b_3_10 + b_1_13·b_1_26·b_3_8 + b_1_14·b_1_23·b_5_22
       + b_1_14·b_1_25·b_3_10 + b_1_14·b_1_25·b_3_8 + b_1_15·b_7_43
       + b_1_15·b_1_22·b_5_22 + b_1_15·b_1_24·b_3_8 + b_1_17·b_1_22·b_3_8
       + b_1_17·b_1_25 + b_1_18·b_1_2·b_3_10 + b_1_18·b_1_2·b_3_8 + b_1_19·b_3_8
       + b_1_19·b_1_23 + b_1_110·b_1_22 + b_6_32·b_3_8·b_3_10 + b_6_32·b_1_23·b_3_10
       + b_6_32·b_1_1·b_5_22 + b_6_32·b_1_1·b_1_22·b_3_10 + b_6_32·b_1_1·b_1_22·b_3_8
       + b_6_32·b_1_13·b_3_8 + b_6_32·b_1_13·b_1_23 + b_6_32·b_1_14·b_1_22
       + b_6_32·b_1_15·b_1_2 + b_6_32·b_1_16 + b_4_16·b_1_25·b_3_8 + b_4_16·b_1_1·b_7_43
       + b_4_16·b_1_1·b_1_24·b_3_10 + b_4_16·b_1_1·b_1_27 + b_4_16·b_1_12·b_1_2·b_5_22
       + b_4_16·b_1_12·b_1_23·b_3_8 + b_4_16·b_1_12·b_1_26
       + b_4_16·b_1_13·b_1_22·b_3_10 + b_4_16·b_1_13·b_1_25 + b_4_16·b_1_14·b_1_24
       + b_4_16·b_1_15·b_3_10 + b_4_16·b_1_18 + b_4_16·b_6_32·b_1_1·b_1_2
       + b_4_16·b_6_32·b_1_12 + b_4_162·b_1_2·b_3_9 + b_4_162·b_1_2·b_3_8
       + b_4_162·b_1_24 + b_4_162·b_1_1·b_3_8 + b_4_162·b_1_1·b_1_23
       + b_4_162·b_1_12·b_1_22 + b_4_162·b_1_13·b_1_2 + b_4_162·b_1_14
       + b_2_4·b_4_16·b_1_2·b_5_23 + b_2_4·b_4_16·b_1_2·b_5_22 + b_2_4·b_2_5·b_4_162
       + b_2_42·b_4_16·b_1_2·b_3_9 + b_2_42·b_4_162 + b_2_43·b_1_2·b_5_23
       + b_2_43·b_1_2·b_5_22 + b_2_43·b_6_32 + b_2_44·b_1_2·b_3_9 + b_2_45·b_2_5 + b_2_46
       + b_2_44·a_1_0·b_3_9 + b_2_44·b_2_5·a_1_0·b_1_2 + c_8_57·b_1_12·b_1_22
       + c_8_57·b_1_14
  48. b_5_23·b_7_43 + b_5_22·b_7_43 + b_1_29·b_3_10 + b_1_212 + b_1_1·b_1_28·b_3_10
       + b_1_12·b_3_10·b_7_43 + b_1_14·b_1_23·b_5_22 + b_1_14·b_1_28 + b_1_15·b_7_43
       + b_1_15·b_1_22·b_5_22 + b_1_15·b_1_24·b_3_10 + b_1_15·b_1_24·b_3_8
       + b_1_15·b_1_27 + b_1_16·b_1_23·b_3_10 + b_1_16·b_1_23·b_3_8 + b_1_17·b_5_22
       + b_1_19·b_3_10 + b_1_19·b_3_8 + b_1_110·b_1_22 + b_6_32·b_3_8·b_3_10
       + b_6_32·b_1_26 + b_6_32·b_1_1·b_5_22 + b_6_32·b_1_1·b_1_22·b_3_10
       + b_6_32·b_1_1·b_1_22·b_3_8 + b_6_32·b_1_1·b_1_25 + b_6_32·b_1_12·b_1_24
       + b_6_32·b_1_13·b_3_10 + b_6_32·b_1_13·b_3_8 + b_6_32·b_1_13·b_1_23
       + b_6_32·b_1_14·b_1_22 + b_6_32·b_1_15·b_1_2 + b_6_32·b_1_16 + b_6_322
       + b_4_16·b_1_23·b_5_22 + b_4_16·b_1_28 + b_4_16·b_1_1·b_7_43
       + b_4_16·b_1_1·b_1_22·b_5_22 + b_4_16·b_1_1·b_1_24·b_3_10
       + b_4_16·b_1_1·b_1_24·b_3_8 + b_4_16·b_1_12·b_1_23·b_3_10
       + b_4_16·b_1_12·b_1_23·b_3_8 + b_4_16·b_1_13·b_5_22 + b_4_16·b_1_13·b_1_25
       + b_4_16·b_1_14·b_1_2·b_3_8 + b_4_16·b_1_15·b_3_10 + b_4_16·b_1_15·b_3_8
       + b_4_16·b_1_15·b_1_23 + b_4_16·b_1_16·b_1_22 + b_4_16·b_1_17·b_1_2
       + b_4_16·b_1_18 + b_4_16·b_6_32·b_1_22 + b_4_162·b_1_2·b_3_10 + b_4_162·b_1_24
       + b_4_162·b_1_1·b_3_10 + b_4_162·b_1_1·b_3_8 + b_4_162·b_1_1·b_1_23
       + b_4_162·b_1_12·b_1_22 + b_4_162·b_1_13·b_1_2 + b_4_162·b_1_14 + b_4_163
       + b_2_4·b_4_16·b_6_32 + b_2_4·b_2_5·b_4_162 + b_2_42·b_4_16·b_1_2·b_3_9
       + b_2_42·b_4_162 + b_2_42·b_2_5·b_6_32 + b_2_44·b_1_2·b_3_10 + b_2_45·b_2_5
       + b_2_46 + b_2_44·a_1_0·b_3_10 + b_2_44·a_1_0·b_3_9 + b_2_44·b_2_5·a_1_0·b_1_2
       + c_8_57·b_1_24 + c_8_57·b_1_12·b_1_22 + b_2_42·c_8_57
  49. b_5_23·b_7_43 + b_1_27·b_5_22 + b_1_29·b_3_8 + b_1_12·b_1_25·b_5_22
       + b_1_12·b_1_27·b_3_8 + b_1_12·b_1_210 + b_1_13·b_1_2·b_3_10·b_5_22
       + b_1_13·b_1_29 + b_1_14·b_1_2·b_7_43 + b_1_14·b_1_23·b_5_22 + b_1_14·b_1_28
       + b_1_15·b_1_22·b_5_22 + b_1_15·b_1_24·b_3_8 + b_1_16·b_3_8·b_3_10
       + b_1_16·b_1_2·b_5_22 + b_1_16·b_1_23·b_3_8 + b_1_16·b_1_26 + b_1_17·b_5_22
       + b_1_17·b_1_22·b_3_8 + b_1_17·b_1_25 + b_1_18·b_1_2·b_3_10 + b_6_32·b_3_8·b_3_10
       + b_6_32·b_1_23·b_3_10 + b_6_32·b_1_1·b_5_22 + b_6_32·b_1_1·b_1_22·b_3_8
       + b_6_32·b_1_1·b_1_25 + b_6_32·b_1_12·b_1_2·b_3_10 + b_6_32·b_1_12·b_1_2·b_3_8
       + b_6_32·b_1_13·b_3_10 + b_6_32·b_1_14·b_1_22 + b_6_32·b_1_15·b_1_2
       + b_4_16·b_3_10·b_5_22 + b_4_16·b_1_2·b_7_43 + b_4_16·b_1_25·b_3_8
       + b_4_16·b_1_1·b_1_24·b_3_10 + b_4_16·b_1_1·b_1_24·b_3_8
       + b_4_16·b_1_12·b_3_8·b_3_10 + b_4_16·b_1_12·b_1_2·b_5_22
       + b_4_16·b_1_12·b_1_23·b_3_10 + b_4_16·b_1_13·b_1_22·b_3_8
       + b_4_16·b_1_13·b_1_25 + b_4_16·b_1_14·b_1_2·b_3_10 + b_4_16·b_1_15·b_3_10
       + b_4_16·b_1_18 + b_4_16·b_6_32·b_1_12 + b_4_162·b_1_2·b_3_10
       + b_4_162·b_1_2·b_3_8 + b_4_162·b_1_1·b_3_10 + b_4_162·b_1_12·b_1_22
       + b_4_162·b_1_14 + b_2_4·b_4_16·b_6_32 + b_2_4·b_2_5·b_4_162
       + b_2_42·b_4_16·b_1_2·b_3_10 + b_2_42·b_4_16·b_1_2·b_3_9 + b_2_43·b_1_2·b_5_22
       + b_2_44·b_1_2·b_3_10 + b_2_44·a_1_0·b_3_10 + b_2_44·b_2_5·a_1_0·b_1_2
       + c_8_57·b_1_1·b_3_8 + c_8_57·b_1_1·b_1_23 + c_8_57·b_1_13·b_1_2
       + b_2_5·c_8_57·a_1_0·b_1_2
  50. b_1_210·b_3_10 + b_1_12·b_1_28·b_3_10 + b_1_13·b_1_25·b_5_22
       + b_1_13·b_1_27·b_3_8 + b_1_14·b_1_2·b_3_10·b_5_22 + b_1_14·b_1_24·b_5_22
       + b_1_15·b_3_10·b_5_22 + b_1_15·b_1_23·b_5_22 + b_1_16·b_7_43
       + b_1_16·b_1_22·b_5_22 + b_1_16·b_1_24·b_3_8 + b_1_17·b_1_23·b_3_10
       + b_1_17·b_1_23·b_3_8 + b_1_17·b_1_26 + b_1_18·b_5_22 + b_1_18·b_1_22·b_3_10
       + b_1_18·b_1_22·b_3_8 + b_1_19·b_1_2·b_3_10 + b_1_19·b_1_2·b_3_8
       + b_1_110·b_1_23 + b_6_32·b_7_43 + b_6_32·b_1_1·b_1_23·b_3_10
       + b_6_32·b_1_12·b_5_22 + b_6_32·b_1_13·b_1_2·b_3_10 + b_6_32·b_1_14·b_3_10
       + b_6_32·b_1_14·b_1_23 + b_6_322·b_1_2 + b_4_16·b_1_24·b_5_22
       + b_4_16·b_1_26·b_3_8 + b_4_16·b_1_1·b_1_2·b_7_43 + b_4_16·b_1_1·b_1_25·b_3_10
       + b_4_16·b_1_1·b_1_25·b_3_8 + b_4_16·b_1_13·b_1_2·b_5_22
       + b_4_16·b_1_13·b_1_23·b_3_10 + b_4_16·b_1_14·b_1_22·b_3_8
       + b_4_16·b_1_15·b_1_2·b_3_10 + b_4_16·b_1_16·b_3_10 + b_4_16·b_1_16·b_3_8
       + b_4_16·b_1_19 + b_4_16·b_6_32·b_3_10 + b_4_16·b_6_32·b_1_1·b_1_22
       + b_4_16·b_6_32·b_1_12·b_1_2 + b_4_162·b_5_23 + b_4_162·b_1_12·b_3_8
       + b_4_162·b_1_14·b_1_2 + b_2_42·b_2_5·b_6_32·b_1_2 + b_2_43·b_6_32·b_1_2
       + b_2_43·b_4_16·b_3_10 + b_2_43·b_4_16·b_3_9 + b_2_44·b_5_23 + b_2_44·b_4_16·b_1_2
       + b_2_45·b_2_5·b_1_2 + b_2_44·a_1_0·b_1_2·b_3_9 + c_8_57·b_1_22·b_3_8
       + c_8_57·b_1_1·b_1_24 + c_8_57·b_1_12·b_3_8 + c_8_57·b_1_15
  51. b_7_432 + b_1_12·b_1_29·b_3_8 + b_1_13·b_1_28·b_3_10 + b_1_13·b_1_211
       + b_1_14·b_3_10·b_7_43 + b_1_14·b_1_25·b_5_22 + b_1_14·b_1_27·b_3_10
       + b_1_14·b_1_27·b_3_8 + b_1_15·b_1_24·b_5_22 + b_1_15·b_1_29
       + b_1_16·b_1_23·b_5_22 + b_1_16·b_1_25·b_3_8 + b_1_17·b_7_43
       + b_1_17·b_1_22·b_5_22 + b_1_17·b_1_24·b_3_8 + b_1_18·b_1_2·b_5_22
       + b_1_18·b_1_26 + b_1_19·b_5_22 + b_1_19·b_1_22·b_3_10 + b_1_110·b_1_2·b_3_10
       + b_1_111·b_3_10 + b_1_111·b_3_8 + b_1_111·b_1_23 + b_6_32·b_1_2·b_7_43
       + b_6_32·b_1_1·b_7_43 + b_6_32·b_1_1·b_1_22·b_5_22 + b_6_32·b_1_1·b_1_24·b_3_8
       + b_6_32·b_1_12·b_1_2·b_5_22 + b_6_32·b_1_12·b_1_23·b_3_8
       + b_6_32·b_1_13·b_1_22·b_3_10 + b_6_32·b_1_13·b_1_22·b_3_8
       + b_6_32·b_1_14·b_1_2·b_3_8 + b_6_32·b_1_14·b_1_24 + b_6_32·b_1_15·b_3_10
       + b_6_32·b_1_15·b_3_8 + b_6_32·b_1_15·b_1_23 + b_6_32·b_1_16·b_1_22
       + b_6_322·b_1_22 + b_4_16·b_1_25·b_5_22 + b_4_16·b_1_27·b_3_8 + b_4_16·b_1_210
       + b_4_16·b_1_1·b_1_24·b_5_22 + b_4_16·b_1_12·b_3_10·b_5_22
       + b_4_16·b_1_12·b_1_25·b_3_8 + b_4_16·b_1_12·b_1_28 + b_4_16·b_1_13·b_7_43
       + b_4_16·b_1_13·b_1_27 + b_4_16·b_1_14·b_1_23·b_3_10
       + b_4_16·b_1_14·b_1_23·b_3_8 + b_4_16·b_1_15·b_1_22·b_3_10
       + b_4_16·b_1_15·b_1_22·b_3_8 + b_4_16·b_1_16·b_1_2·b_3_10
       + b_4_16·b_1_16·b_1_2·b_3_8 + b_4_16·b_1_16·b_1_24 + b_4_16·b_1_17·b_3_8
       + b_4_16·b_6_32·b_1_2·b_3_10 + b_4_16·b_6_32·b_1_1·b_3_10 + b_4_16·b_6_32·b_1_1·b_3_8
       + b_4_16·b_6_32·b_1_12·b_1_22 + b_4_16·b_6_32·b_1_13·b_1_2
       + b_4_162·b_1_2·b_5_23 + b_4_162·b_1_23·b_3_10 + b_4_162·b_1_1·b_5_22
       + b_4_162·b_1_1·b_1_22·b_3_10 + b_4_162·b_1_1·b_1_22·b_3_8
       + b_4_162·b_1_1·b_1_25 + b_4_162·b_1_14·b_1_22 + b_4_162·b_1_16
       + b_4_163·b_1_22 + b_4_163·b_1_1·b_1_2 + b_4_163·b_1_12
       + b_2_4·b_4_162·b_1_2·b_3_9 + b_2_42·b_2_5·b_4_162 + b_2_43·b_4_16·b_1_2·b_3_10
       + b_2_43·b_4_16·b_1_2·b_3_9 + b_2_43·b_2_5·b_6_32 + b_2_44·b_1_2·b_5_23
       + b_2_44·b_6_32 + b_2_45·b_1_2·b_3_10 + b_2_46·b_2_5 + b_2_45·a_1_0·b_3_10
       + b_2_45·a_1_0·b_3_9 + c_8_57·b_1_23·b_3_8 + c_8_57·b_1_1·b_1_25
       + c_8_57·b_1_12·b_1_2·b_3_10 + c_8_57·b_1_12·b_1_24 + c_8_57·b_1_13·b_3_10
       + c_8_57·b_1_15·b_1_2 + c_8_57·b_1_16 + b_4_16·c_8_57·b_1_12

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Data used for Benson′s test

  • Benson′s completion test succeeded in degree 17.
  • However, the last relation was already found in degree 14 and the last generator in degree 8.
  • The following is a filter regular homogeneous system of parameters:
    1. c_8_57, a Duflot regular element of degree 8
    2. b_1_2·b_3_10 + b_1_2·b_3_9 + b_1_2·b_3_8 + b_1_1·b_3_10 + b_1_1·b_3_8 + b_1_1·b_1_23
         + b_1_12·b_1_22 + b_1_14 + b_4_16 + b_2_4·b_2_5 + b_2_42, an element of degree 4
    3. b_1_2·b_5_23 + b_1_2·b_5_22 + b_1_23·b_3_8 + b_1_1·b_1_22·b_3_10 + b_1_1·b_1_22·b_3_8
         + b_1_1·b_1_25 + b_1_12·b_1_2·b_3_10 + b_1_12·b_1_24 + b_1_13·b_3_10
         + b_1_13·b_3_8 + b_1_13·b_1_23 + b_1_14·b_1_22 + b_4_16·b_1_22
         + b_4_16·b_1_1·b_1_2 + b_4_16·b_1_12 + b_2_4·b_4_16 + b_2_42·b_2_5, an element of degree 6
    4. b_1_1·b_1_23·b_3_10 + b_1_1·b_1_26 + b_1_12·b_1_22·b_3_8 + b_1_13·b_1_2·b_3_10
         + b_1_13·b_1_2·b_3_8 + b_1_13·b_1_24 + b_4_16·b_1_1·b_1_22 + b_4_16·b_1_12·b_1_2
         + b_2_5·b_4_16·b_1_2 + b_2_4·b_5_23 + b_2_42·b_3_10, an element of degree 7
  • The Raw Filter Degree Type of that HSOP is [-1, -1, 7, 14, 21].
  • The filter degree type of any filter regular HSOP is [-1, -2, -3, -4, -4].
  • We found that there exists some filter regular HSOP formed by the first term of the above HSOP, together with 3 elements of degree 4.

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Restriction maps

Restriction map to the greatest central el. ab. subgp., which is of rank 1

  1. a_1_0 → 0, an element of degree 1
  2. b_1_1 → 0, an element of degree 1
  3. b_1_2 → 0, an element of degree 1
  4. b_2_4 → 0, an element of degree 2
  5. b_2_5 → 0, an element of degree 2
  6. b_3_8 → 0, an element of degree 3
  7. b_3_9 → 0, an element of degree 3
  8. b_3_10 → 0, an element of degree 3
  9. b_4_16 → 0, an element of degree 4
  10. b_5_22 → 0, an element of degree 5
  11. b_5_23 → 0, an element of degree 5
  12. b_6_32 → 0, an element of degree 6
  13. b_7_43 → 0, an element of degree 7
  14. c_8_57 → c_1_08, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 3

  1. a_1_0 → 0, an element of degree 1
  2. b_1_1 → 0, an element of degree 1
  3. b_1_2 → c_1_2, an element of degree 1
  4. b_2_4 → c_1_22, an element of degree 2
  5. b_2_5 → 0, an element of degree 2
  6. b_3_8 → 0, an element of degree 3
  7. b_3_9 → c_1_1·c_1_22 + c_1_12·c_1_2, an element of degree 3
  8. b_3_10 → 0, an element of degree 3
  9. b_4_16 → c_1_1·c_1_23 + c_1_14, an element of degree 4
  10. b_5_22 → c_1_12·c_1_23 + c_1_14·c_1_2, an element of degree 5
  11. b_5_23 → 0, an element of degree 5
  12. b_6_32 → c_1_1·c_1_25 + c_1_13·c_1_23 + c_1_15·c_1_2 + c_1_16, an element of degree 6
  13. b_7_43 → c_1_12·c_1_25 + c_1_13·c_1_24 + c_1_15·c_1_22 + c_1_16·c_1_2, an element of degree 7
  14. c_8_57 → c_1_13·c_1_25 + c_1_15·c_1_23 + c_1_16·c_1_22 + c_1_18
       + c_1_02·c_1_12·c_1_24 + c_1_02·c_1_14·c_1_22 + c_1_04·c_1_24
       + c_1_04·c_1_12·c_1_22 + c_1_04·c_1_14 + c_1_08, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 3

  1. a_1_0 → 0, an element of degree 1
  2. b_1_1 → 0, an element of degree 1
  3. b_1_2 → c_1_2, an element of degree 1
  4. b_2_4 → c_1_22, an element of degree 2
  5. b_2_5 → c_1_22, an element of degree 2
  6. b_3_8 → 0, an element of degree 3
  7. b_3_9 → c_1_23 + c_1_1·c_1_22 + c_1_12·c_1_2, an element of degree 3
  8. b_3_10 → c_1_23 + c_1_1·c_1_22 + c_1_12·c_1_2, an element of degree 3
  9. b_4_16 → c_1_24 + c_1_12·c_1_22 + c_1_14, an element of degree 4
  10. b_5_22 → c_1_25 + c_1_1·c_1_24 + c_1_12·c_1_23, an element of degree 5
  11. b_5_23 → c_1_1·c_1_24 + c_1_14·c_1_2, an element of degree 5
  12. b_6_32 → c_1_26 + c_1_12·c_1_24 + c_1_13·c_1_23 + c_1_15·c_1_2 + c_1_16, an element of degree 6
  13. b_7_43 → c_1_1·c_1_26 + c_1_12·c_1_25 + c_1_13·c_1_24 + c_1_14·c_1_23
       + c_1_15·c_1_22 + c_1_16·c_1_2, an element of degree 7
  14. c_8_57 → c_1_28 + c_1_1·c_1_27 + c_1_13·c_1_25 + c_1_14·c_1_24 + c_1_15·c_1_23
       + c_1_16·c_1_22 + c_1_18 + c_1_02·c_1_12·c_1_24 + c_1_02·c_1_14·c_1_22
       + c_1_04·c_1_24 + c_1_04·c_1_12·c_1_22 + c_1_04·c_1_14 + c_1_08, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 4

  1. a_1_0 → 0, an element of degree 1
  2. b_1_1 → c_1_1, an element of degree 1
  3. b_1_2 → c_1_3, an element of degree 1
  4. b_2_4 → 0, an element of degree 2
  5. b_2_5 → 0, an element of degree 2
  6. b_3_8 → c_1_33 + c_1_1·c_1_22 + c_1_12·c_1_3 + c_1_12·c_1_2, an element of degree 3
  7. b_3_9 → c_1_33 + c_1_1·c_1_22 + c_1_12·c_1_3 + c_1_12·c_1_2, an element of degree 3
  8. b_3_10 → c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_1·c_1_22 + c_1_12·c_1_2 + c_1_0·c_1_12
       + c_1_02·c_1_1, an element of degree 3
  9. b_4_16 → c_1_34 + c_1_2·c_1_33 + c_1_24 + c_1_1·c_1_22·c_1_3 + c_1_12·c_1_22
       + c_1_13·c_1_3 + c_1_0·c_1_12·c_1_3 + c_1_0·c_1_13 + c_1_02·c_1_1·c_1_3
       + c_1_02·c_1_12, an element of degree 4
  10. b_5_22 → c_1_35 + c_1_2·c_1_34 + c_1_24·c_1_3 + c_1_1·c_1_34 + c_1_13·c_1_32
       + c_1_14·c_1_3 + c_1_0·c_1_14 + c_1_04·c_1_1, an element of degree 5
  11. b_5_23 → c_1_35 + c_1_22·c_1_33 + c_1_24·c_1_3 + c_1_1·c_1_2·c_1_33
       + c_1_1·c_1_22·c_1_32 + c_1_12·c_1_2·c_1_32 + c_1_13·c_1_32
       + c_1_13·c_1_2·c_1_3 + c_1_0·c_1_12·c_1_32 + c_1_0·c_1_13·c_1_3
       + c_1_02·c_1_1·c_1_32 + c_1_02·c_1_12·c_1_3 + c_1_02·c_1_13 + c_1_04·c_1_1, an element of degree 5
  12. b_6_32 → c_1_2·c_1_35 + c_1_26 + c_1_1·c_1_2·c_1_34 + c_1_1·c_1_24·c_1_3 + c_1_1·c_1_25
       + c_1_12·c_1_22·c_1_32 + c_1_13·c_1_22·c_1_3 + c_1_13·c_1_23
       + c_1_14·c_1_32 + c_1_14·c_1_2·c_1_3 + c_1_15·c_1_2 + c_1_0·c_1_1·c_1_34
       + c_1_0·c_1_13·c_1_32 + c_1_0·c_1_14·c_1_3 + c_1_0·c_1_15 + c_1_02·c_1_34
       + c_1_02·c_1_13·c_1_3 + c_1_04·c_1_32 + c_1_04·c_1_12, an element of degree 6
  13. b_7_43 → c_1_2·c_1_36 + c_1_22·c_1_35 + c_1_23·c_1_34 + c_1_24·c_1_33
       + c_1_25·c_1_32 + c_1_26·c_1_3 + c_1_1·c_1_36 + c_1_1·c_1_23·c_1_33
       + c_1_1·c_1_24·c_1_32 + c_1_1·c_1_26 + c_1_12·c_1_22·c_1_33 + c_1_12·c_1_25
       + c_1_13·c_1_34 + c_1_13·c_1_2·c_1_33 + c_1_13·c_1_22·c_1_32
       + c_1_13·c_1_23·c_1_3 + c_1_13·c_1_24 + c_1_14·c_1_22·c_1_3 + c_1_14·c_1_23
       + c_1_15·c_1_32 + c_1_15·c_1_2·c_1_3 + c_1_15·c_1_22 + c_1_16·c_1_3
       + c_1_16·c_1_2 + c_1_0·c_1_12·c_1_24 + c_1_0·c_1_13·c_1_22·c_1_3
       + c_1_0·c_1_14·c_1_2·c_1_3 + c_1_0·c_1_15·c_1_3 + c_1_0·c_1_15·c_1_2
       + c_1_02·c_1_1·c_1_24 + c_1_02·c_1_12·c_1_22·c_1_3 + c_1_02·c_1_13·c_1_32
       + c_1_02·c_1_13·c_1_2·c_1_3 + c_1_02·c_1_13·c_1_22 + c_1_04·c_1_1·c_1_32
       + c_1_04·c_1_1·c_1_22 + c_1_04·c_1_12·c_1_3 + c_1_04·c_1_12·c_1_2, an element of degree 7
  14. c_8_57 → c_1_38 + c_1_22·c_1_36 + c_1_23·c_1_35 + c_1_24·c_1_34 + c_1_25·c_1_33
       + c_1_26·c_1_32 + c_1_28 + c_1_1·c_1_37 + c_1_1·c_1_2·c_1_36
       + c_1_1·c_1_22·c_1_35 + c_1_1·c_1_26·c_1_3 + c_1_12·c_1_22·c_1_34
       + c_1_12·c_1_23·c_1_33 + c_1_12·c_1_24·c_1_32 + c_1_12·c_1_25·c_1_3
       + c_1_12·c_1_26 + c_1_13·c_1_2·c_1_34 + c_1_13·c_1_22·c_1_33
       + c_1_13·c_1_23·c_1_32 + c_1_13·c_1_24·c_1_3 + c_1_13·c_1_25
       + c_1_14·c_1_34 + c_1_14·c_1_2·c_1_33 + c_1_14·c_1_22·c_1_32
       + c_1_14·c_1_23·c_1_3 + c_1_15·c_1_2·c_1_32 + c_1_15·c_1_23 + c_1_16·c_1_32
       + c_1_16·c_1_22 + c_1_17·c_1_3 + c_1_17·c_1_2 + c_1_0·c_1_1·c_1_22·c_1_34
       + c_1_0·c_1_1·c_1_24·c_1_32 + c_1_0·c_1_14·c_1_22·c_1_3
       + c_1_0·c_1_15·c_1_2·c_1_3 + c_1_02·c_1_22·c_1_34 + c_1_02·c_1_24·c_1_32
       + c_1_02·c_1_12·c_1_34 + c_1_02·c_1_12·c_1_22·c_1_32
       + c_1_02·c_1_12·c_1_24 + c_1_02·c_1_13·c_1_22·c_1_3 + c_1_02·c_1_14·c_1_22
       + c_1_02·c_1_15·c_1_3 + c_1_02·c_1_16 + c_1_03·c_1_15 + c_1_04·c_1_34
       + c_1_04·c_1_22·c_1_32 + c_1_04·c_1_24 + c_1_04·c_1_12·c_1_2·c_1_3
       + c_1_04·c_1_12·c_1_22 + c_1_04·c_1_13·c_1_3 + c_1_04·c_1_14
       + c_1_05·c_1_13 + c_1_06·c_1_12 + c_1_08, an element of degree 8

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128


Simon A. King David J. Green
Fakultät für Mathematik und Informatik Fakultät für Mathematik und Informatik
Friedrich-Schiller-Universität Jena Friedrich-Schiller-Universität Jena
Ernst-Abbe-Platz 2 Ernst-Abbe-Platz 2
D-07743 Jena D-07743 Jena
Germany Germany
E-mail: simon dot king at uni hyphen jena dot de
Tel: +49 (0)3641 9-46184
Fax: +49 (0)3641 9-46162
Office: Zi. 3524, Ernst-Abbe-Platz 2
E-mail: david dot green at uni hyphen jena dot de
Tel: +49 3641 9-46166
Fax: +49 3641 9-46162
Office: Zi 3512, Ernst-Abbe-Platz 2

Last change: 25.08.2009